How much of that walk around time is just time saving from other things?
I'm also called productive by my team and I do the same as I save so much time by not having to deal with interruptions, leaving meetings on in the background, and and being able to work through lunch.
None of the walkaround time is saved from other things I'd say. I don't work through lunch, my lunch break has gotten longer because I make food instead of eating in the canteen, and lunch is one of the enjoyable times when I do not feel guilty for not working. The 'enjoyable because I do not feel guilty for not working' is somewhat true for the meetings now as well.
I'm also called productive by my team and I do the same as I save so much time by not having to deal with interruptions, leaving meetings on in the background, and and being able to work through lunch.